A214777 McNugget numbers: numbers of the form 6*x + 9*y + 20*z for nonnegative integers x, y, z.

0, 6, 9, 12, 15, 18, 20, 21, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset

1,2

Comments

A214772(a(n)) > 0;

complement of A065003; all numbers greater than 43 are McNugget numbers: Frobenius(6,9,20) = 43.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Scott Chapman, Christopher O'Neill, Factoring in the Chicken McNugget monoid, arXiv:1709.01606 [math.AC], 2017.

Anita Wah and Henri Picciotto, Lesson in Algebra: Themes, Tools, Concepts

Eric Weisstein's World of Mathematics, Frobenius Number.

Eric Weisstein's World of Mathematics, McNugget Numbers.

Wikipedia, Coin problem

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: -x^2*(x^22-x^21+x^17-x^16+x^15-x^14+x^13-x^12+x^11-x^10+x^9+x^8-2*x^7+x^6+x^5+3*x-6) / (x-1)^2. [Colin Barker, Dec 13 2012]

a(n) = n + 21 for n >= 23. - Robert Israel, May 01 2015

Mathematica

CoefficientList[Series[- x (x^22 - x^21 + x^17 - x^16 + x^15 - x^14 + x^13 - x^12 + x^11 - x^10 + x^9 + x^8 - 2 x^7 + x^6 + x^5 + 3 x - 6)/(1 - x)^2, {x, 0, 70}], x] (* Vincenzo Librandi, Apr 27 2015 *)

Prog

(Haskell)
import Data.List (findIndices)
a214777 n = a214777_list !! (n-1)
a214777_list = findIndices (> 0) a214772_list

Crossrefs

Sequence in context: A262828 A306647 A189728 * A239310 A130699 A099862

Adjacent sequences: A214774 A214775 A214776 * A214778 A214779 A214780

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jul 28 2012

Status

approved